Abstract
A famous result of Freiman describes the structure of finite sets A {subseteq} Z with small doubling property. If |A + A| ≤ K|A|, then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.
| Translated title of the contribution | Freiman's theorem in an arbitrary abelian group |
|---|---|
| Original language | English |
| Pages (from-to) | 163 - 175 |
| Number of pages | 13 |
| Journal | Journal of the London Mathematical Society |
| Volume | 75 (1) |
| DOIs | |
| Publication status | Published - Feb 2007 |